解方程2sin3x·cos2x+2sin^2x=0

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/16 13:00:46
解方程2sin3x·cos2x+2sin^2x=0
x){|i;6*38=9بBċ35I*'HΆH4| M8c- # Mm$Q#$KMxg˞U@ѩakЂjX;z]h.&mXLPj# !?:RoS(RakhkkWahk}A|>`H,Sa Sa_\g;

解方程2sin3x·cos2x+2sin^2x=0
解方程2sin3x·cos2x+2sin^2x=0

解方程2sin3x·cos2x+2sin^2x=0
2*(sin(x))^3*cos(2*x)+2*(sin(x))^2=0
解析:左式= 2*(sin(x))^3*(1-2(sin(x))^2)+2*(sin(x))^2
= 2*(sin(x))^3-4*(sin(x))^5+2*(sin(x))^2
= [sin(x)-2*(sin(x))^3+1]2*(sin(x))^2
=(sin(x)-1)*(-2*(sin(x))^2-2*sin(x)-1)*2*(sin(x))^2=0
∵-2*(sin(x))^2-2*sin(x)-1<0
∴sinx=1==>x1=2kπ+π/2
Sinx=0==>x2=2kπ,x3=2kπ+π